SOLUTION: In a three digit number, the difference between the hundreds and tens digits is equal to that of the tens and units digit. also, the sum of the digits is nine. How many numbers are

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Question 980638: In a three digit number, the difference between the hundreds and tens digits is equal to that of the tens and units digit. also, the sum of the digits is nine. How many numbers are possible which satisfy the above given condition?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
the difference between the hundreds and tens digits is equal to
that of the tens and units digit. 
      h-t = t-u
(1)   h+u = 2t

the sum of the digits is nine
    h+t+u = 9
(2)   h+u = 9-t 

       2t = 9-t   because they both equal to h+u in (1) and (2)
       3t = 9
        t = 3

So the middle digit (the tens digit) is 3.
So the first and last digits must have sum 6 in order for all
three digits to have sum 9.

So the possibilities are these 6:

135
234
333
432
531
630

Edwin